Resource rents and models for taxation of these rents. Some references to the situation for Greenland. After a general introduction to the concept of rents the risk of distortion by double taxation of the normal capital income to investment is explained. Cash flow taxation or deduction in the tax base of investment times the risk free interest rate can be used to avoid this double taxation. Among other instruments to secure a part of rents for the public sector are direct participation and selling rights to exploit the resources by auction. The greater part of the paper is about taxation of rents in fisheries. The regulation is assumed to be based on professional advising and individual transferable quotas. Duties on the quota or a general cost increasing tariff, e. g. on fuel, are administratively simple models for taxation. Cost increasing indirect taxation has the good quality of incentive compatibility, as it supports the effort reducing aim of regulation. A concrete example illustrates a possible taxation of the prawn/shrimp fishery combining a duty on the quota with a tariff levied on the catch. Some comment are given on a recent report on the shrimp fishery (2005), and it is criticised for highlighting the theoretical qualities of Greenland’s fisheries policy, but neglecting the regulation and also to which extent incomes derived from quotas end up as income for Greenlandic households.